Low-energy QCD

We derive a low-energy quantum field theory from quantum chromodynamics (QCD) that holds in the limit of a very large coupling. All the parameters of the bare theory are fixed through QCD. Low-energy limit is obtained through a mapping theorem between massless quartic scalar field theory and Yang-Mills theory. One gets a Yukawa theory that, in the same limit of strong coupling, reduces to a Nambu-Jona-Lasinio model with a current-current coupling with scalar-like excitations arising from Yang-Mills degrees of freedom. A current-current expansion in the strong coupling limit yields a fully integrated generating functional that, neglecting quark-quark current coupling, describes all processes involving glue excitations and quark. Some processes are analyzed and we are able to show consistency of Narison-Veneziano sum rules. Width of the $\sigma$ resonance is computed. The decay $\eta'\to\eta+\pi^++\pi^-$ is discussed in this approximation and analyzed through the more elementary processes $\eta'\to\eta+\sigma$ and $\sigma\to\pi^++\pi^-$. In this way we get an estimation of the mass of the $\sigma$ resonance and the value of the $\eta$ decay constant. This $\eta'$ decay appears a possible source of study for the $\sigma$ resonance.